# Rodion Kuzmin

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Template:Infobox scientist
**Rodion Osievich Kuzmin** (Russian: Родион Осиевич Кузьмин{{#invoke:Category handler|main}}, Nov. 9, 1891, Riabye village in the Haradok district – March 23, 1949, Leningrad) was a Russian mathematician, known for his works in number theory and analysis.^{[1]} His name is sometimes transliterated as Kusmin.

## Selected results

- In 1928, Kuzmin solved
^{[2]}the following problem due to Gauss (see Gauss–Kuzmin distribution): if*x*is a random number chosen uniformly in (0, 1), and

- is its continued fraction expansion, find a bound for
- where
- Gauss showed that
*Δ*_{n}tends to zero as*n*goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that - where
*C*,*α*> 0 are numerical constants. In 1929, the bound was improved to*C*0.7^{n}by Paul Lévy.

- In 1930, Kuzmin proved
^{[3]}that numbers of the form*a*^{b}, where*a*is algebraic and*b*is a real quadratic irrational, are transcendental. In particular, this result implies that Gelfond–Schneider constant

- is transcendental. See Gelfond–Schneider theorem for later developments.

- He is also known for the Kusmin-Landau inequality: If is continuously differentiable with monotonic derivative satisfying (where denotes the Nearest integer function) on a finite interval , then

## Notes

## External links

- Rodion Kuzmin at the Mathematics Genealogy Project (The chronology there is apparently wrong, since J. V. Uspensky lived in USA from 1929.)